If creating a vector field based on an equation is not possible, how create an equation-free 3-D vector field in blender?

The arrows should have color based on the magnitude of force they exert on objects. It would be great if the Vector field, can actually exert forces.

I understand that it's not possible to list everything in a single answer, but if someone can guide me in the right direction, it would be highly helpful.

Something like this

Something like this

EDIT: Someone has actually done this, I precisely want to do something like this. https://www.reddit.com/r/blender/comments/8aqyns/vector_field/?utm_source=share&utm_medium=web2x

  • $\begingroup$ Could you please elaborate. Does the result need to be renderable, animatable, and how many roundabouts? $\endgroup$ – batFINGER Oct 29 '19 at 6:58
  • $\begingroup$ @batFINGER I exactly want something like the picture, I just have to look at the field from various angles. It would be nice, if it actually exerts a force on a object placed in the field. I primarily want to show arrows whose color is based on the magnitude obtained from a equation. $\endgroup$ – Aravindh Vasu Oct 29 '19 at 7:02
  • 2
    $\begingroup$ The simplest of gizmos is an arrow. See text editor > templates > python > gizmo simple which displays an arrow gizmo to control the intensity of a spot lamp when selected. The color and orientation of the gizmo arrow can be set. This will display on 3d view as in image, but not be renderable, or animated using standard keyframing or drivers. A point cloud mesh (verts only) could be used for positions, and vertex color layer (rgba) for magnitude and direction of vector. $\endgroup$ – batFINGER Oct 29 '19 at 9:39
  • $\begingroup$ @batFINGER thank you, I'm totally new so please bare with me. I'm having blender 2.79, there is no option named "gizmo simple" in the menu. $\endgroup$ – Aravindh Vasu Oct 29 '19 at 9:43
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    $\begingroup$ Oh ok, gizmos are new in 2.8. Similarly in pre 2.8 could use bgl to draw arrows. Similarly to normals overlay $\endgroup$ – batFINGER Oct 29 '19 at 10:01

You could use mesh arrows to do it.

First, you need to create an arrow and the object that controls the field (in my case an empty named CTRL), then add a Track To constraint that points to the control.

Then you'll need to create your grid, which can do using this script:

import bpy
from bpy.app.handlers import persistent

dim = 10   #number of arrows on an edge og the cubic grid
spacing = 1
ctrl = bpy.data.objects["CTRL"]     #the control object
maxScale = 0.2
minScale = 0.01
distRange = 5

obj = bpy.context.selected_objects[0]

parent_coll = bpy.context.selected_objects[0].users_collection[0]
coll = bpy.data.collections.new("Grid")
for i in range(dim):
    for j in range(dim):
        for k in range(dim):
            new_obj = obj.copy()
            #new_obj.data = obj.data.copy()
            new_obj.location = ((i-dim/2)*spacing, (j-dim/2)*spacing, (k-dim/2)*spacing)  #define arrows positions (here they are centered on the world origin)

            #add drivers on the scale
            for t in range(3):
                driv = new_obj.driver_add("scale", t).driver
                driv.type = 'SCRIPTED'
                driv.use_self = True

                dist = driv.variables.new()
                dist.name = "ctrlName"
                dist.type = 'SINGLE_PROP'
                dist.targets[0].id = ctrl
                dist.targets[0].data_path = "name"

                driv.expression = "getScale(ctrlName, self, "+str(maxScale)+","+str(minScale)+","+str(distRange)+")"

def getScale(ctrlName, obj, maxScale, minScale, distRange):
    ctrl = bpy.data.objects[ctrlName]
    dist = getDistance(ctrl, obj)
    power = ctrl.scale[0]
    scaleRange = maxScale - minScale
    dist = dist/power   #distance is affected by the control size as well

    if dist > distRange:
        scale = minScale
        scale = scaleRange/(distRange**2)*(dist**2) - 2*scaleRange/distRange*dist + maxScale    #Here you define your scale function

    return scale

def getDistance(ctrl, obj):
    sum = 0
    for i in range(3):
        sum += (ctrl.location[i] - obj.location[i])**2
    return sum**0.5

bpy.app.driver_namespace['getScale'] = getScale

The first part takes care of duplicating the arrows on the grid. As you can see, at the top there are some parameters you can change without going too much into the code.

The second part of the script creates and runs the drivers that control the scale of the arrows: it's a function that takes some of the parameters at the top of the script and calculates the scale of every single arrow. I strongly suggest you to check and modify the function to fit your needs, expecially if you are working on a scientific project.

The way I set it up is using a normal quadratic interpolation:

enter image description here

this is not very good looking, but you'll have the pick the interpolation you prefer. Also, note that in the script the size of the control affects the field as well.

For the color, there is just one material that calculates the distance between each arrow and the control (the control's position is gathered with 3 drivers) and feeds it in a ColorRamp

enter image description here

This is the final result with the download link of the project:

enter image description here

There are many things that can be changed or improved, but I stopped here because this might be enough for you. Possible changes could be a different interpolation function for the scale or the color (because right now they work on a 2 different interpolations, but it's possible to join them together); some custom properties to store the parameters in the GUI, so that you don't have to run the script again every time you make a change; you could want to change only the length of the arrow instead of all 3 dimensions; etc...

After an extensive correspondence we came up with a broader solution, available on Github at https://github.com/Hilicot/Blender-Field-Generator

  • $\begingroup$ Thank you very much, I'm totally interested in full script. $\endgroup$ – Aravindh Vasu Oct 29 '19 at 16:03
  • $\begingroup$ @AravindhVasu I edited the answer, tell me what you think of it $\endgroup$ – Tareyes Oct 29 '19 at 21:44
  • $\begingroup$ Wow thank you very much. To be honest, I'm fairly new to blender. So, it will take some time for me to understand everything. Is there anyway to contact you, if I get stuck somewhere(Probably at many places)? $\endgroup$ – Aravindh Vasu Oct 30 '19 at 0:04
  • $\begingroup$ Is it possible to create a similar field governed by an equation? $\endgroup$ – Aravindh Vasu Oct 30 '19 at 0:46
  • $\begingroup$ I don't understand how the color for the arrows are determined, are they determined based on the distance from the control object or based on their size? I wanted all the arrows to be somewhat of the same size visually to avoid clutter, so I used the sigmoid function. I wanted colour to give a vague sense of their actual size $\endgroup$ – Aravindh Vasu Oct 30 '19 at 4:02

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